Greece's leftist Syriza party has a 0.5 percentage-point lead over the conservative New Democracy party before a snap election on Sept. 20, according to a poll published on Monday.

Former prime minister Alexis Tsipras's Syriza is on course to win 27 percent of the vote and New Democracy should get 26.5 percent, the poll by Pulse for the bankingnews.gr website found.

Despite everything, the country has been through in recent months, it is thought that Tsipras himself remains quite popular

Tsipras started out as the frontrunner in the race, but the two parties have been neck-and-neck in recent polls, making the election unexpectedly close.

Two polls over the weekend also put Syriza marginally ahead, even though its lead is shrinking. Two other polls published last week showed New Democracy beating Syriza for the first time.

In Monday's poll, the far-right Golden Dawn party, whose leader and senior lawmakers are standing trial on charges of being a criminal group, ranked third with 6.5 percent of the vote.

The Independent Greeks, Tsipras's junior coalition partner, is expected to get 2.5 percent of the vote, below the 3 percent threshold needed to enter parliament.

As many as 35 percent of Greeks want the two first parties to form a coalition government, the poll showed. Tsipras has so far ruled out doing any such deal with New Democracy. His opponent, Evangelos Meimarakis, has said he is open to cooperating.